Title: Degenerate cubic nonlinear susceptibility tensor in an isotropic medium and its determination

Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportionalmore » to two different elliptic Jacobi functions with the same periods. (nonlinear optical phenomena)« less

For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor {Chi}{sup 2} (z, 2{omega}; {omega}, {omega}) responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of themore » wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.« less

Research was carried out investigating the feasibility of using a regional distance seismic waveform moment tensor inverse procedure to estimate source parameters of nuclear explosions and to use the source inversion results to develop a source-type discrimination capability. The results of the research indicate that it is possible to robustly determine the seismic moment tensor of nuclear explosions, and when compared to natural seismicity in the context of the a Hudson et al. (1989) source-type diagram they are found to separate from populations of earthquakes and underground cavity collapse seismic sources.

Two different force constant models are studied numerically in order to determine the elastic energy wave number characteristics (EWNC) for cubic crystals when the linear-expansion-coefficient tensors are anisotropically diagonalized. For the previously offered model (Model I) a general expression for EWNC is derived. A new model (Model II) based on nearest-neighbor coupling is presented. EWNC for Fe, Ni and Cu are numerically calculated for both models. The different models generally yield different EWNC's for the same case. However, the values of the EWNC at the origin of the first Brillouin zone (the continuum limit) are always model independent and agreemore » with those calculated by the linear continuum theory of elasticity. (auth)« less

We welcome the Comment by Lerche et al on our recent paper titled "A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions." The Comment brings up additional historical facts about previous research on the infinite sums of products of Bessel functions appearing in the plasma susceptibility.